Then that brings rise to an industry producing and selling breathable air! Think of all the jobs this would create and how it would boom the economy!
It would also end all crime, because the government simply could forbid selling breathable air to criminals. Think of the amount of money we all could save without prisons existing!
Oxygen is highly reactive so there's a replenishment mechanism at play to maintain the 20% we know and love in the atmosphere. Of course, if the phytoplankton give up the ghost that will end poorly for anything that likes to respire, but that's a completely different problem and would be as much of an existential issue with or without "white hydrogen" energy.
Oxygen is the waste product of obtaining hydrogen from water.
Plants can help balance that, but we're also busy deteriorating plant life.
When you burn carbon (coal) and produce CO2, you get about 400 kJ for each mole of CO2 produced. When you burn hydrogen, you get about 300 kJ for each mole, but one molecule of water H2O contains half the oxygen of one molecule of CO2. So you get 600 kJ for 2 moles, which contain the same amount of oxygen as one mole of CO2. In other words, when you burn hydrogen you produce 50% more energy than when you burn carbon for the same amount of oxygen removed from the atmosphere.
Since the start of the industrial revolution we've increased the CO2 in the atmosphere from 280 ppm to 420 ppm, or an increase of 140 ppm (parts per million). Which means we've reduced the oxygen in the atmosphere by 140 ppm (each molecule of CO2 produced removes a molecule of O2). A quick google shows me there's 20.947% of oxygen in the atmosphere. Which means before the industrial revolution we had 20.947% + 0.014% = 20.961% oxygen. If we wave a magic want, and rewrite history so that all coal and fossil fuels were replaced by pure hydrogen, then we would have removed only about two thirds of the oxygen, or about 90 ppm. So we would have had more oxygen, not less. By about 0.005%, or 20.952%.
In any case, I don't think any impact on life would be felt whatsoever if the concentration of oxygen is 20.952% rather than 20.947%.